{
  "id": 3124,
  "curve_key": "28585284696938182729860469648763386643443423213521:-179197671874547709773162710616140488959750915566836338050334541353488492569",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-595526764519545473538759784349237221738404650282",
    "207404712817763552978197730613335214330524536966377034126822264871403881"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    4
  ],
  "naive_height": 341.94923240851244,
  "faltings_height": 26.487176727883053,
  "conductor": "7882602549544199351275160289497567761080531375360072630",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "23",
    "29",
    "47",
    "73",
    "113",
    "173",
    "229",
    "251",
    "751",
    "1861",
    "2351",
    "3919",
    "4007",
    "4639",
    "42569",
    "134999",
    "321569"
  ],
  "discriminant": "-5066111468274005125739393545635032946710399655806922507181320810609494960253843205840030246924030839517365353390752509497488200105984000000000000",
  "regulator": "6131817773001.05627778498541356324890199962580209313293138217",
  "points": [
    [
      "124724020384798220345041",
      "367516581253672140997126646108909079"
    ],
    [
      "15324897121776184029316609/49",
      "78023030459275713874593021865060671697/343"
    ],
    [
      "28612989853882985666849529/169",
      "733385789605154435150615291385098596963/2197"
    ],
    [
      "840079999716341125193632180425/395641",
      "726227720407682224612892525839435956289462763/248858189"
    ],
    [
      "-1584048856742125556157627017391/1803649",
      "-557746031527477128709154863569311707980857047/2422300607"
    ],
    [
      "263385382871596577215041",
      "-262341765294032260000723764046834121"
    ],
    [
      "27280404387326409806039629900561/159744321",
      "671707802680359923079182200461092289035487008201/2019008473119"
    ],
    [
      "466825184386555940312841",
      "-176439935634864282815841693878298521"
    ],
    [
      "319445922309616026821601",
      "-223078905661744788924733733911327961"
    ],
    [
      "678051177799205539879839686345375311005885921/1508904437607749867281",
      "-10242265179139088732174481695367570720017471057776400624129966398559/58612818226198120621463239836679"
    ],
    [
      "25248366306029966967837632925/32041",
      "-2735196341107935781267239092724000780378727/5735339"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "2-isogenous image of D-z2z2old1011121314-055, rational kernel x=7261995732809195702276475/4. Source: https://dujella.github.io/tors/z2z2old1011121314.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.",
  "created_at": "2026-09-26 20:38:23",
  "updated_at": "2026-09-26 20:38:23"
}